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Related Concept Videos

Confidence Coefficient01:24

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...
Confidence Intervals01:21

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...

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Related Experiment Videos

A SIMULTANEOUS CONFIDENCE BAND FOR SPARSE LONGITUDINAL REGRESSION.

Shujie Ma1, Lijian Yang, Raymond J Carroll

  • 1Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824.

Statistica Sinica
|March 6, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for creating confidence bands in functional regression models. The approach, using piecewise constant spline estimation, is validated through simulations and applied to HIV patient data.

Keywords:
B splineKarhunen-Loève L2 representationconfidence bandfunctional dataknotslongitudinal datastrong approximation

Related Experiment Videos

Area of Science:

  • Statistics
  • Biostatistics
  • Functional Data Analysis

Background:

  • Functional data analysis is gaining prominence with numerous successful applications.
  • Understanding the mean function in functional regression is crucial for accurate modeling.

Purpose of the Study:

  • To develop asymptotically simultaneous confidence bands for the mean function in functional regression models.
  • To provide a robust statistical tool for analyzing longitudinal data.

Main Methods:

  • Piecewise constant spline estimation was employed for modeling.
  • Asymptotic theory was used to derive the confidence bands.
  • Simulation experiments were conducted to validate the theoretical findings.

Main Results:

  • The proposed confidence band procedure demonstrated effectiveness in simulations.
  • The method accurately captures uncertainty in the mean function estimation.
  • The analysis of CD4 cell counts in HIV patients showcased the practical application.

Conclusions:

  • The developed confidence bands offer a reliable method for functional regression analysis.
  • This technique is valuable for interpreting complex functional data, such as in clinical studies.
  • The study confirms the utility of piecewise constant spline estimation in this context.